Following is a partial list of published methods for reservoir characterization using different metrics.
U.S. Pat. No. 6,438,493 (“Method for Seismic Facies Interpretation Using Textural Analysis and Neural Networks”) to West and May discloses a method for segmentation based on seismic texture classification. For a prescribed set of seismic facies in seismic data volume, textural attributes are calculated and used to train a probabilistic neural network. This neural network is then used to classify each voxel of the data, which in practice segments the data into the different classes.
Further, U.S. Pat. No. 6,560,540 (“Method for Mapping Seismic Attributes Using Neural Networks”) to West and May disclose a method for classification of seismic data during the seismic facies mapping process.
U.S. Pat. No. 6,278,949 (“Method for Multi-Attribute Identification of Structure and Stratigraphy in a Volume of Seismic Data”) to Alam discloses a method for the visual exploration of a seismic volume without horizon picking or editing, but that still displays all horizons with their stratigraphic features and lithologic variations. Seismic data are processed to generate multiple attributes at each event location with a specified phase of the seismic trace. Subsets of multiple attributes are then interactively selected, thresholded, and combined with a mathematical operator into a new volume displayed on a computer workstation. Manipulation of attribute volumes and operators allows the user to visually recognize bodies of potential hydrocarbon reservoirs.
U.S. Pat. No. 6,631,202 (“Method for Aligning a Lattice of Points in Response to Features in a Digital Image”) to Hale discloses a method for generating a lattice of points that respect features such as surfaces or faults in a seismic data volume. Hale and Emanuel further disclosed methods (“Atomic Meshing of Seismic Images”, SEG Expanded Abstracts 21, 2126-2129 (2002); and “Seismic interpretation using global image segmentation”, SEG Expanded Abstracts 22, 2410-2413 (2003)), to segment a data volume by creation of a space-filling polyhedral mesh based on this lattice.
U.S. Pat. No. 7,024,021 (“Method for Performing Stratigraphically-Based Seed Detection in a 3D Seismic Data Volume”) to Dunn and Czernuszenko discloses a method for performing a stratigraphically-based seed detection in a 3-D seismic data volume. The method honors the layered nature of the subsurface so that the resulting geobodies are stratigraphically reasonable. The method can either extract all geobodies that satisfy specified criteria or determine the size and shape of a specific geobody in a seismic data volume.
U.S. Pat. No. 7,248,539 (“Extrema Classification”) to Borgos et al. discloses a method for the automated extraction of surface primitives from seismic data. The steps include construction of seismic surfaces through an extrema representation of a 3D seismic data; computation of waveform attributes near the extrema, and classification based on these attributes to extract surface pieces. Pieces are then combined into horizon interpretations, used for the definition of surfaces or the estimation of fault displacements.
U.S. Patent Application 2007/0036434 (“Topology-Based Method of Partition, Analysis, and Simplification of Dynamical Images and Its Applications”) by Saveliey discloses a method for the topological analysis and decomposition of dynamical images through computation of homology groups to be used, for example, for image enhancement or pattern recognition. A dynamical image is an array of black-and-white images (or frames) of arbitrary dimension that are constructed from gray scale and color images, or video sequences. Each frame is partitioned into a collection of components that are linked to the ones in adjacent frames to record how they merge and split.
U.S. Patent Application 2008/0037843 (“Image Segmentation for DRR Generation and Image Registration”) by Fu et al. discloses a method for enhancing the multi-dimensional registration with digitally reconstructed radiographs derived from segmented x-ray data.
U.S. Patent Application 2008/0140319 (“Processing of Stratigraphic Data”) by Monsen et al. discloses a method of processing stratigraphic data, such as horizon surfaces, within a geological volume. The method assigns to each stratigraphic feature a relative geological age by construction of a graph structure which is used for interpretation.
U.S. Patent Application 2008/0170756 (“Method for Hierarchical Determination of Coherent Events in a Seismic Image”) by Beucher et al. discloses a method for the determination of coherent events in a seismic image which employs a hierarchical segmentation based on the watershed algorithm to track coherent surfaces.
U.S. Patent Application 2008/0243749 (“System and Method for Multiple Volume Segmentation”) by Petter et al. discloses a method for performing oilfield operations which co-renders a visually-melded scene from two different seismic datasets. The visually-melded scene comprises a visualized geobody that is used to adjust oilfield operations.
U.S. Patent Applications 2010/0149917, 2010/0161232, 2011/0002194, and 2011/0048731 (“Seismic Horizon Skeletonization”) by Imhof et al. disclose a method that extracts all surfaces from a seismic volume simultaneously. The resulting seismic skeleton is stratigraphically and topologically consistent.
Pitas and Kotropoulos (“Texture Analysis and Segmentation of Seismic Images”, International Conference on Acoustics, Speech, and Signal Processing, 1437-1440 (1989)) propose a method for the texture analysis and segmentation of geophysical data based on the detection of seismic horizons and the calculation of their attributes (e.g. length, average reflection strength, signature). These attributes represent the texture of the seismic image. The surfaces are clustered into classes according to these attributes. Each cluster represents a distinct texture characteristic of the seismic image. After this initial clustering, the points of each surface are used as seeds for segmentation where all pixels in the seismic image are clustered in those classes in accordance to their geometric proximity to the classified surfaces.
Simaan (e.g., “Knowledge-Based Computer System for Segmentation of Seismic Sections Based on Texture”, SEG Expanded Abstracts 10, 289-292 (1991)) discloses a method for the segmentation of two-dimensional seismic sections based on the seismic texture and heuristic geologic rules.
Fernandez et al. (“Texture Segmentation of a 3D Seismic Section with Wavelet Transform and Gabor Filters”, 15th International Conference on Pattern Recognition, 354-357 (2000)) describe a supervised segmentation (i.e., classification) of a 3D seismic section that is carried out using wavelet transforms. Attributes are computed on the wavelet expansion and on the wavelet-filtered signal, and used by a classifier to recognize and subsequently segment the seismic section. The filters are designed by optimizing the classification of geologically well understood zones. As a result of the segmentation, zones of different internal stratification are identified in the seismic section by comparison with the reference patterns extracted from the representative areas.
Valet et al. (“Seismic Image Segmentation by Fuzzy Fusion of Attributes”, IEEE Transactions On Instrumentation And Measurement 50(4), 1014-1018 (2001)) present a method for seismic segmentation based on the fusion of different attributes by using a set of rules expressed by fuzzy theory. The attributes are based on the eigenvalues of the structure tensor and measure total energy and dip-steered discontinuity. The final result is segmentation into high-amplitude continuous layers, chaotic regions, and background.
Monsen and Ødegård disclose a method for the segmentation of seismic data in “Segmentation of Seismic Data with Complex Stratigraphy Using Watershedding—Preliminary Results” in the proceedings of IEEE 10th Digital Signal Processing Workshop, and the 2nd Signal Processing Education Workshop (2002). The seismic data are treated as a topographic map. All the minima in the relief are slowly flooded. When the water level from different floods merges, dams are built to stop the flood from spilling into different domains. The flooding is continued until all of the relief is covered. The ultimate segmentation is then given by the dams that have built. The problem with the watershed algorithm is its inherent tendency to over-segment due to small, local minima. Progressive removal of small minima yields a hierarchical multiresolution segmentation of nested segments.
Further, Monsen et al. (“Multi-scale volume model building”, SEG Expanded Abstracts 24, 798-801 (2005)) disclose a method for automated hierarchical model building with the promise of multi-scale model consistency. No further details are disclosed, however.
Faucon et al. (“Morphological Segmentation Applied to 3D Seismic Data”, in Mathematical Morphology: 40 Years On, Computational Imaging and Vision, Volume 30, 475-484 (2005)) present the results obtained by carrying out hierarchal segmentation on 3D seismic data. First, they performed a marker-based segmentation of a seismic amplitude cube constrained by a previously picked surface. Second, they applied a hierarchical segmentation to the same data without a priori information about surfaces.
Lomask et al. (“Application Of Image Segmentation To Tracking 3D Salt Boundaries”, Geophysics 72, P47-56 (2007)) present a method to delineate salt from sediment using normalized cuts image segmentation that finds the boundaries between dissimilar regions of the data. The method calculates a weight connecting each pixel in the image to every other pixel within a local neighborhood. The weights are determined using a combination of instantaneous amplitude and instantaneous dip attributes. The weights for the entire date are used to segment the image via an eigenvector calculation.
Kadlec et al., (“Confidence and Curvature-Guided Level Sets for Channel Segmentation”, SEG Expanded Abstracts 27, 879-883 (2008)) present a method for segmenting channel features from 3D seismic volumes based on the local structure tensor.
Patel et al., (“The Seismic Analyzer: Interpreting And Illustrating 2D Seismic Data”, IEEE Transactions On Visualization And Computer Graphics 14(6), 1571-1578 (2008)) disclose a toolbox for the interpretation and illustration of two-dimensional seismic slices. The method precalculates the horizon structures in the seismic data and annotates them by applying illustrative rendering algorithms such as deformed texturing and line and texture transfer functions.
U.S. Pat. No. 6,757,217 (“Method for time-aligning multiple offset seismic data volumes”) by Eastwood et al. discloses a method to time align multiple seismic data volumes based on the cross-correlation of the data volumes at a plurality of time shifts.
Bronstein, Alexander M et al., (“Efficient Computation of Isometry-Invarient Distances Between Surfaces”, SIAM J. Sci. Comput. 28(5), 1812-1836 (2006)) describe an efficient computational framework for isometry-invariant comparison of smooth surfaces.
Zhu, Binhai, (“Protein Local Structure Alignment Under the Discrete Fréchet Distance,” J. of Computational Biology 14(10), 1342-1351 (2007)) studies the complexity and algorithmic aspects of local protein structure alignment under the discrete Fréchet distance.
Alt, Helmut and Maike Buchin, (“Can We Compute the Similarity Between Surfaces?,” Discrete and Computational Geometry 43(1) (2010)) provide an introduction and disclose the limitations of the Hausdorff distance metric and provide a computable characterization of the weak Fréchet distance in a geometric data structure called a free space diagram.